N.H. Rev. Stat. § 660:3
Any candidate for whom a vote was cast for any office at a state general election, provided that the difference between the votes cast for the applying candidate and a candidate declared elected is less than 20 percent of the total votes cast in the towns which comprise the office to be recounted, shall be entitled to apply for only one recount under this chapter, and the declaration made by the secretary of state under RSA 660:6 shall be final, subject to a change in the result following an appeal to the ballot law commission, as provided in RSA 665:8, II. If more than one candidate for the same office in the same district applies for a recount under this chapter, and a recount is completed, such applications shall not result in a second recount.
RSA 660:3
1979, 436:1. 1983, 175:3. 2003, 151:3. 2008, 377:4, eff. Sept. 9, 2008.